In the mounting of a riflescope upon the barrel of a rifle it is of utmost importance that provision be made for "zeroing in" the scope which is the process by which the line-of-sight established by the reticle in the scope that defines the point of impact of the bullet be made coincident with the axis of the bore at some preselected range, say 150 yards. While most, if not all, riflescopes provide limited adjustments to correct for windage and elevation, these should not have to be used, and in most cases are insufficient, to make gross adjustments to zero in the scope initially. Instead, lateral and vertical adjustments in the mounting hardware by means of which the scope is attached to the rifle barrel should provide the means for making such corrections and, once made, they should remain fixed. Certain rifle manufacturers, Ruger for one, make their so-called "receiver" integral with the barrel and since the scope mounting rings attach to this receiver, if it is significantly misaligned in any way with respect to the bore axis, there is no way of correcting the misaligned condition except for the rings themselves. Up until now at least, the scope mounting rings supplied by the rifle manufacturer include no such adjustment feature and, in addition, are considerably more complicated and expensive to manufacture than they need to be.